Analysis of Single Server Markovian Queue with Balking,Reneging and Rejoining of customers under Multiple Vacationpolicy

Abstract

In this paper, we investigate a single-server Markovian queuing model considering cus-
tomer’s impatience under multiple vacation policy. The server does not provide service to
customers during vacation periods, and customers may either renege or balk in this state.
During active state, customers neither renege nor balk. Additionally, the queuing system has
a notification mechanism where the system notifies all balked customer that the server is ac-
tive. As a result, a fraction of balked customer may rejoin the system with certain probability
again forming an additional input stream along with the regular arrival of customer. Various
system parameters has been presented to evaluate system efficiency. Sensitivity analysis is
performed to examine the impact of system parameters on different performance measures.
A cost model is framed on the proposed queuing model on which we apply Genetic Algo-
rithm (GA) to determine the minimum cost and optimal values for system parameters. This
approach aids management in optimizing customer service while maintaining cost efficiency.